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A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We show that the relativistic effects are negligibly small in the non-linear density and velocity bispectra. Although the non-linearities of Einstein equation introduce additional non-linear terms to the Newtonian fluid equations, the…
We consider the propagation of wave packets for a nonlinear Schr\"odinger equation, with a matrix-valued potential, in the semi-classical limit. For a matrix-valued potential, Strichartz estimates are available under long range assumptions.…
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the…
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Linear and nonlinear optical effect has been widely discussed in large quantity of materials using theoretical or experimental methods. Except linear optical conductivity, higher-order nonlinear responses are not studied fully. Starting…
When supersymmetry is spontaneously broken it will be generically non-linearly realized. A method to describe the non-linear realization of supersymmetry is with constrained superfields. We discuss the basic features of this description and…
A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property,…
In this paper we establish the existence of certain classes of solutions to the energy critical nonlinear wave equation in dimensions 3 and 5 assuming that the energy exceeds the ground state energy only by a small amount. No radial…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
One of the possible applications of macroscopic Einstein equations has been considered. So, the nonsingular isotropic and uniform cosmological model is built. The cosmological consequences of this model are agree with conclusions of…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most…
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. It has been a long-standing open problem in astrophysics for…